(For background and current purpose of this question, please see here: Prevent page break within \item of an enumerate).
I have an enumerate of questions. Each of those questions has some opening text and then a nested enumerate. I give an example below that results in a page-break in the middle of the second question in the PDF output. I mark with \newpage where I would like the page-break to be (automatically) inserted. In this particular example, I want the first question to be on page 1, and the second and third to be on page 2 (just because they both happen to fit).
There are some answers at Prevent page break within \item of an enumerate, but I would like a LyX-specific solution, and I do not want to redefine \item because \item is used besides just the enumerate environment. I would like something that works on the LyX layout level so that I can either use it as a module, or local layout, without changing any of the contents of the body.
Here is a LyX minimal example:
#LyX 2.3 created this file. For more info see http://www.lyx.org/
\lyxformat 544
\begin_document
\begin_header
\save_transient_properties true
\origin unavailable
\textclass article
\begin_preamble
%% my attempt:
%\let\OldItem\item
%\renewcommand{\item}{\OldItem \ifnum \@listdepth=1 \begin{samepage}\fi}
%\AfterEndEnvironment{enumerate}{\ifnum \@listdepth=1 \end{samepage}\fi}
\end_preamble
\use_default_options false
\maintain_unincluded_children false
\language english
\language_package none
\inputencoding auto
\fontencoding default
\font_roman "default" "default"
\font_sans "default" "default"
\font_typewriter "default" "default"
\font_math "auto" "auto"
\font_default_family default
\use_non_tex_fonts false
\font_sc false
\font_osf false
\font_sf_scale 100 100
\font_tt_scale 100 100
\use_microtype false
\use_dash_ligatures true
\graphics default
\default_output_format default
\output_sync 0
\bibtex_command default
\index_command default
\paperfontsize default
\spacing single
\use_hyperref false
\papersize default
\use_geometry false
\use_package amsmath 1
\use_package amssymb 0
\use_package cancel 0
\use_package esint 1
\use_package mathdots 0
\use_package mathtools 0
\use_package mhchem 0
\use_package stackrel 0
\use_package stmaryrd 0
\use_package undertilde 0
\cite_engine basic
\cite_engine_type default
\biblio_style plain
\use_bibtopic false
\use_indices false
\paperorientation portrait
\suppress_date false
\justification true
\use_refstyle 0
\use_minted 0
\index Index
\shortcut idx
\color #008000
\end_index
\secnumdepth 3
\tocdepth 3
\paragraph_separation indent
\paragraph_indentation default
\is_math_indent 0
\math_numbering_side default
\quotes_style english
\dynamic_quotes 0
\papercolumns 1
\papersides 1
\paperpagestyle default
\tracking_changes false
\output_changes false
\html_math_output 0
\html_css_as_file 0
\html_be_strict false
\end_header
\begin_body
\begin_layout Enumerate
2 + 2 = ?
\begin_inset Newline newline
\end_inset
filler
\begin_inset Newline newline
\end_inset
filler
\begin_inset Newline newline
\end_inset
filler
\begin_inset Newline newline
\end_inset
filler
\begin_inset Newline newline
\end_inset
filler
\begin_inset Newline newline
\end_inset
filler
\begin_inset Newline newline
\end_inset
filler
\begin_inset Newline newline
\end_inset
filler
\begin_inset Newline newline
\end_inset
filler
\begin_inset Newline newline
\end_inset
filler
\begin_inset Newline newline
\end_inset
filler
\begin_inset Newline newline
\end_inset
filler
\begin_inset Newline newline
\end_inset
filler
\begin_inset Newline newline
\end_inset
filler
\begin_inset Newline newline
\end_inset
filler
\begin_inset Newline newline
\end_inset
filler
\begin_inset Newline newline
\end_inset
filler
\begin_inset Newline newline
\end_inset
filler
\begin_inset Newline newline
\end_inset
filler
\begin_inset Newline newline
\end_inset
filler
\begin_inset Newline newline
\end_inset
filler
\begin_inset Newline newline
\end_inset
filler
\begin_inset Newline newline
\end_inset
filler
\begin_inset Newline newline
\end_inset
filler
\end_layout
\begin_deeper
\begin_layout Enumerate
1
\end_layout
\begin_layout Enumerate
2
\end_layout
\begin_layout Enumerate
3
\end_layout
\begin_layout Enumerate
4
\end_layout
\begin_layout Standard
\begin_inset ERT
status collapsed
\begin_layout Plain Layout
% I do not want to put this page break in manually:
\end_layout
\begin_layout Plain Layout
\end_layout
\end_inset
\begin_inset ERT
status collapsed
\begin_layout Plain Layout
%
\backslash
newpage
\end_layout
\begin_layout Plain Layout
\end_layout
\end_inset
\end_layout
\end_deeper
\begin_layout Enumerate
Consider the joint probability distribution below: filler
\begin_inset Newline newline
\end_inset
filler
\begin_inset Newline newline
\end_inset
filler
\begin_inset Newline newline
\end_inset
filler
\begin_inset Newline newline
\end_inset
filler
\begin_inset Newline newline
\end_inset
filler
\begin_inset Newline newline
\end_inset
filler
\begin_inset Newline newline
\end_inset
filler
\end_layout
\begin_deeper
\begin_layout Standard
\align center
\begin_inset Tabular
<lyxtabular version="3" rows="3" columns="3">
<features tabularvalignment="middle">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<column alignment="center" valignment="top">
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $X_{2}=0$
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $X_{2}=1$
\end_inset
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $X_{1}=0$
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $\frac{1}{10}$
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $\frac{3}{10}$
\end_inset
\end_layout
\end_inset
</cell>
</row>
<row>
<cell alignment="center" valignment="top" topline="true" bottomline="true" leftline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $X_{1}=1$
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $\frac{2}{10}$
\end_inset
\end_layout
\end_inset
</cell>
<cell alignment="center" valignment="top" topline="true" bottomline="true" rightline="true" usebox="none">
\begin_inset Text
\begin_layout Plain Layout
\begin_inset Formula $\frac{4}{10}$
\end_inset
\end_layout
\end_inset
</cell>
</row>
</lyxtabular>
\end_inset
\end_layout
\begin_layout Standard
What is
\begin_inset Formula $P(X_{1}=1)$
\end_inset
?
\end_layout
\begin_layout Enumerate
I do not know.
\end_layout
\begin_layout Enumerate
4
\end_layout
\begin_layout Enumerate
17
\end_layout
\begin_layout Enumerate
88
\end_layout
\end_deeper
\begin_layout Enumerate
2 - 2 + 5 = filler
\begin_inset Newline newline
\end_inset
filler
\begin_inset Newline newline
\end_inset
filler
\begin_inset Newline newline
\end_inset
filler
\begin_inset Newline newline
\end_inset
filler
\begin_inset Newline newline
\end_inset
filler
\begin_inset Newline newline
\end_inset
filler
\begin_inset Newline newline
\end_inset
filler
\begin_inset Newline newline
\end_inset
filler
\begin_inset Newline newline
\end_inset
filler
\begin_inset Newline newline
\end_inset
filler
\begin_inset Newline newline
\end_inset
filler
\begin_inset Newline newline
\end_inset
filler
\begin_inset Newline newline
\end_inset
filler
\begin_inset Newline newline
\end_inset
filler
\begin_inset Newline newline
\end_inset
filler
\begin_inset Newline newline
\end_inset
filler
\begin_inset Newline newline
\end_inset
filler
\begin_inset Newline newline
\end_inset
filler
\end_layout
\begin_deeper
\begin_layout Enumerate
1
\end_layout
\begin_layout Enumerate
2
\end_layout
\begin_layout Enumerate
3
\end_layout
\begin_layout Enumerate
4
\end_layout
\end_deeper
\end_body
\end_document
